Applied mathematics-1
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Question paper 1
SECTION-A
Q1. a) Choose the correct answer.i. If nP4 = 20 × nP2 then n is equal to
a) 7 b) 8 c) 2 d) 4Answer:
, 
(a) option
ii. Modulus of 3 – 4i is
a) 6 b) 5 c) 4 d) 3Answer:
b
iii. Slope of line 3x + y – 2 = 0 is
a) 3 b) 2 c) - 3 d) -2Answer:
c
iv. Mid points internally of (-a, b) and (a, -b) is
a)
b)
c) a + bd) (0, 0)
Answer:
d
v. The point (-4, -5) lies in quadrant
a) 1st b) 2nd c) 3rd d) 4thAnswer:
c
b) State True or False.
vi. Sin(A + B) = SinA CosB – CosA SinBAnswer:
False
vii. Sum of first n natural numbers is
Answer:
False
viii. If a, b, c are in A.P then 2b = 2a + c.
Answer:
False
ix. Length of latus rectum of ellipse
+ 
= 1 is 
.Answer:
True
x. The equation 3x + 4y + 5 = 0 and 4x – 3y + 7 = 0 represent perpendicular lines.
Answer:
True
c) Fill in the blanks.
xi. nth term of a G.P is ________Answer:
xii. The eccentricity of parabola is _________
Answer:
1
xiii. The equation x + 2y + 3 = 0 to the slope form is _________
Answer:
xiv. Two lines are ________if their slopes are equal.
Answer:
Parallel
xv. Value of
= ________Answer:
-1
SECTION-B
Q2. Attempt any six questions.
a. If
Show that 
.Answer:
b) Given log2 = .30103, log5 = 0.69897 Solve the equations 2x. 5y = 1, 5x+1. 2y = 2.
Answer:
Equations
Taking log on both sides
Taking log on both sides
Equation 1 multiplying by log 5 and equation 2 by log 2, then subtracting 1 and 2, we get
, 
Ansc. Find the term independent of x in the expansion of
.Answer:
Find the term independent of x in expansion of
Solution :
Let
is the term independent of x.
Term independent of x if
Ansd. Resolve into partial fraction
.Answer:
Resolve into partial fraction
Sol:
e. Express the Complex number -3 + 3i in polar form.
Answer:
Express into
in polar form.
From 1 and 2, we get
From equation 3.
f. Find the co-ordinates of foot of perpendicular from the point (2, 3) on the line y = 3x + 4.
Answer:
The slope of line perpendicular to
g. Prove that
.Answer:
Prove that
Solution :
h. Sum the series 0.9 + 0.09 + 0.009 + ----- to nth term.
Answer:
i. The sum of two angles is
and their difference is 
. Find the angles in degrees and radians.Answer:
SECTION-C
Q3. Attempt any three questions.i. Find the equation of circle which passes through the points (4, 1) and (6, 5) and has its centre lies on the line 4x + y = 16.
Answer:
(ii) If
Answer:
--------1
---------2Squaring and adding 1 and 2
2 sin
2+2
Squaring 1 and 2 and subtranction 1 from 2
Hence Proved(iv) Find the co-ordinates of focus, vertex, the equation of directrix and axis of parabola y2 - 4y – 2x – 8 = 0
Answer:
Equation of parabola is given by
------------1Shift the origin to the point (-6,2) by putting x=x1-6 and y=y1+2
vertex is (0,0)Focus is (12 , 0) and directrix is (
Vertex is (-6,2)
Focus is (-6+
(
Directrix is
X+6=
X= -6-
(v) A boy observes the angle of elevation of a mountain top to be 600 and after walking directly away from it on level ground through 100 meters, the angle of elevation is 450. Find the height of the mountain and the distance between the mountain and first position of the boy.
Answer:
In right angle triangle ABD
1=
h=x -------1
in right angle triangle ACD
--------2From eq 1 and 2 we get :
= 
h (
h =
h =
